26,391 research outputs found
ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers
Solving the electronic structure from a generalized or standard eigenproblem
is often the bottleneck in large scale calculations based on Kohn-Sham
density-functional theory. This problem must be addressed by essentially all
current electronic structure codes, based on similar matrix expressions, and by
high-performance computation. We here present a unified software interface,
ELSI, to access different strategies that address the Kohn-Sham eigenvalue
problem. Currently supported algorithms include the dense generalized
eigensolver library ELPA, the orbital minimization method implemented in
libOMM, and the pole expansion and selected inversion (PEXSI) approach with
lower computational complexity for semilocal density functionals. The ELSI
interface aims to simplify the implementation and optimal use of the different
strategies, by offering (a) a unified software framework designed for the
electronic structure solvers in Kohn-Sham density-functional theory; (b)
reasonable default parameters for a chosen solver; (c) automatic conversion
between input and internal working matrix formats, and in the future (d)
recommendation of the optimal solver depending on the specific problem.
Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800
basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table
A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics
We describe a new Godunov algorithm for relativistic magnetohydrodynamics
(RMHD) that combines a simple, unsplit second order accurate integrator with
the constrained transport (CT) method for enforcing the solenoidal constraint
on the magnetic field. A variety of approximate Riemann solvers are implemented
to compute the fluxes of the conserved variables. The methods are tested with a
comprehensive suite of multidimensional problems. These tests have helped us
develop a hierarchy of correction steps that are applied when the integration
algorithm predicts unphysical states due to errors in the fluxes, or errors in
the inversion between conserved and primitive variables. Although used
exceedingly rarely, these corrections dramatically improve the stability of the
algorithm. We present preliminary results from the application of these
algorithms to two problems in RMHD: the propagation of supersonic magnetized
jets, and the amplification of magnetic field by turbulence driven by the
relativistic Kelvin-Helmholtz instability (KHI). Both of these applications
reveal important differences between the results computed with Riemann solvers
that adopt different approximations for the fluxes. For example, we show that
use of Riemann solvers which include both contact and rotational
discontinuities can increase the strength of the magnetic field within the
cocoon by a factor of ten in simulations of RMHD jets, and can increase the
spectral resolution of three-dimensional RMHD turbulence driven by the KHI by a
factor of 2. This increase in accuracy far outweighs the associated increase in
computational cost. Our RMHD scheme is publicly available as part of the Athena
code.Comment: 75 pages, 28 figures, accepted for publication in ApJS. Version with
high resolution figures available from
http://jila.colorado.edu/~krb3u/Athena_SR/rmhd_method_paper.pd
IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains
This paper proposes an extension of the Multi-Index Stochastic Collocation
(MISC) method for forward uncertainty quantification (UQ) problems in
computational domains of shape other than a square or cube, by exploiting
isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC
algorithm is very natural since they are tensor-based PDE solvers, which are
precisely what is required by the MISC machinery. Moreover, the
combination-technique formulation of MISC allows the straight-forward reuse of
existing implementations of IGA solvers. We present numerical results to
showcase the effectiveness of the proposed approach.Comment: version 3, version after revisio
Integrating continuous differential evolution with discrete local search for meander line RFID antenna design
The automated design of meander line RFID antennas is a discrete self-avoiding walk(SAW) problem for which efficiency is to be maximized while resonant frequency is to beminimized. This work presents a novel exploration of how discrete local search may beincorporated into a continuous solver such as differential evolution (DE). A prior DE algorithmfor this problem that incorporates an adaptive solution encoding and a bias favoringantennas with low resonant frequency is extended by the addition of the backbite localsearch operator and a variety of schemes for reintroducing modified designs into the DEpopulation. The algorithm is extremely competitive with an existing ACO approach and thetechnique is transferable to other SAW problems and other continuous solvers. The findingsindicate that careful reintegration of discrete local search results into the continuous populationis necessary for effective performance
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